Find: int cos^{2} x , dx | vedclass

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Question

(A) We use the trigonometric identity $\cos 2x = 2 \cos^{2} x - 1$,which implies $\cos^{2} x = \frac{1 + \cos 2x}{2}$.Substituting this into the integ

Vedclass · Accepted Answer

$\frac{x}{2} + \frac{1}{4} \sin 2x + C$

Vedclass · Answer

(A) We use the trigonometric identity $\cos 2x = 2 \cos^{2} x - 1$,which implies $\cos^{2} x = \frac{1 + \cos 2x}{2}$.Substituting this into the integral,we get:$\int \cos^{2} x \, dx = \int \frac{1 + \cos 2x}{2} \, dx$$= \frac{1}{2} \int (1 + \cos 2x) \, dx$$= \frac{1}{2} \left( \int 1 \, dx + \int \cos 2x \, dx \right)$$= \frac{1}{2} \left( x + \frac{\sin 2x}{2} \right) + C$$= \frac{x}{2} + \frac{1}{4} \sin 2x + C$

Find: $\int \cos^{2} x \, dx$

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